A Refined Theory For Earthquake-Resistant Design Of Structures

A vast amount of research was focused on the theory of seismic force in the past decades, and the study on the seismic force modification factor based on the displacement ductility is an important branch. The number of the earthquake records used in the early research was much less, and the influence of the frequency property on the seismic force modification factor R was not taken into consideration either. The effect of ductility and the energy-dissipating capacity on factor R were not checked separately. The development of the seismic force modification factor and the R values prescribed in the codes of different countries are reviewed first.Based on elastic-plastic time-history earthquake analysis of SDOF system, total 370 earthquake records belonging to 4 site and soil conditions with each containing 74 to 106 records are used to calculate the structure response. It is found that the characteristic periods corresponding to the acceleration response S_a and the R factor spectra are much different. This paper provides an investigation on the characteristic period of seismic ground motion. Except S_a and R spectra, the maximum input energy S_ei, velocity S_v ,power density P_SD and the Fourier amplitude spectrum F_S were also calculated to decide their characteristic periods. It is found that the characteristic period determined by S_a spectrum is shorter than those determined from the other spectra. The other spectra predict similar characteristic periods. Through analysis of SDOF systems under harmonic excitations, it is found that S_a spectrum is more sensitive to the excitation with a low period. The characteristic periods T_gR and T_ga are used to normalize the seismic force modification factor and the yielding strength coefficient spectra.The seismic force modification factor spectra for the modified-Clough model (MC), elastic-plastic (EPP), shear-slipped (SSP) and bilinear elastic (BIL) are constructed. The influence of dynamic P-Δeffects and the lateral strength on structure stability and the seismic force modification factor are analyzed. The dynamic elastic-plastic response of multi-degree-of-freedom (MDOF) systems with the storey restoring force model of elastic-perfectly plastic (EPP) are calculated. The seismic force modification factors R_MDOF spectra for MDOF system are obtained. Compared to the R_SDOF of SDOF system, the R_M which can account for the MDOF effect on R spectra are calculated. It is found that the R_M is affected by the number of storey, ductility, normalized period T / T_gR, the ratio of storey stiffness and strength.The elastic-plastic displacement response of EPP with the same yield strength under the earthquake action is calculated and the inelastic displacement amplification factor C_d2 are investigated for different normalized period T/T_gR, site types, strength reduction factor R , damping ratio, post yield stiffness ratio and second order (P-Δ) effect. The C_d2 factor can be used to estimatethe maximum inelastic response displacement induced by the design seismic action from the elastic displacement.The ductility response of SDOF system with the same elastic perfectly plastic hysteretic model envelop lines designed according to the seismic fortification intensity (8 degree) is calculated, under the earthquake records with different peak acceleration values. It is found that the shape of histogram of ductility response for the normalized period T/T_gR and seismic force reduction R , is similar to the density function of lognormal distribution, and the density function is fitted. With the probability of exceedance of the seismic fortification intensity, the probability of the ductility demand greater than the corresponding reduction factor R is obtained when the structure experiences the seismic action gentle than the designed seismic fortification intensity.In order to calculate the seismic force simply, two sets of inelastic yielding strength demand factorη_yμ spectra were calculated from statistical analysis by indirect and direct method. The spectra are normalized by the characteristic period T_ga, by which the peak values near the period T_ga are maintained well. The combinedη_yμ spectra with period normalized by T_ga and T_gR and separated to three parts (0ga, T_gagR and T>T_gR) are constructed to keep the peak values at the periods T _ga and T_gR . Because of the stability of the yield displacement in the design process, the Yield Point Spectra (YPS) is proposed to describe the relationship between the yield displacementΔ_y and the inelastic yielding strength coefficient C_y. The YPS is a sort of constant ductility response spectra taking the yield displacementΔ_y as the primary design parameter. It can be used in a seismic design of buildings and also to estimate the maximum inelastic displacement of the structure under the seismic actions.